where \(n_i\ge n_j\) , \(m_i\ge m_j\)  for
\(i>j\) , with \(n_1 m_i - n_i m_1 \ne 0\)  for
\(i\ne 1\) ,
\(f_i\)  and \(f_i^{\prime }\)  are holomorphic functions
of \(u\)  and \(v\) , and \(f_i = o(z_1)\) , and
the \(g_i\)  are local units (are holomorphic with
non-zero constant terms in their series expansions),
see [1]}.
We refer the reader to [2]} for
background information on the resolution
of singularities via quadratic transformations.
